At high level, you gain magical items.
There are several very useful magical items that require you to spend your bonus action:
Bag of Tricks
Boots of Speed
Necklace of Prayer Beads
Quaal's Feather Token (whip, 1 use)
Scimitar of Speed
So all other things being equal, the TWF guy won't be able to benefit as much from those.
Let's compare ...
Normal Attack action plus one as a bonus action
The Dual Wielder feat does not grant any additional attacks. Its main benefit is allowing you to use Two-Weapon Fighting with non-light weapon, thereby increasing your damage output. It has the additional benefit of allowing you to draw two weapons at a time, allowing you to get around the one free item ...
You can take the Attack action once and make another attack as a bonus action.
(Note the uppercase-A vs. lowercase-a attacks, there.)
You can take the Attack action, as one does. Per "Two-Weapon Fighting" (PHB 195) when anyone does that with a light, one-handed weapon they can make a second attack as a bonus action with another light, one-handed weapon in ...
What if it was two pointy shields?
The idea is to have a strong defense and a nice damage, dealing a half-stab/falf-blunt damage, not only bashing using the shields face, being able to still do great damage using Holy Smite.
A "weapon" that, if someone attacks you from the rear while you're attaking someone, you could just retract your arm and simply block ...